Simplifying / finding common denominators / Mixed operations: Practice Questions

Evaluate the expression: \( \left( 3\frac{1}{2} + 2.25 \right) \times \frac{4}{23} \).

Simplify the following expression: \( \left( 2\frac{2}{3} + 1\frac{1}{2} \right) \div \frac{5}{6} - 1\frac{1}{4} \times 2 \).

Evaluate the following mixed operation with fractions: \( 2\frac{2}{3} + 1\frac{1}{2} \times \frac{4}{9} \).

Simplify the following expression: \( [ 1\frac{3}{4} + ( 2.5 \times \frac{4}{5} ) ] \div ( 0.6 - \frac{1}{10} ) \).

Calculate the exact value of \( (3\frac{1}{3} - 1\frac{1}{2}) \div (1\frac{5}{6} + \frac{2}{3}) \) and express it in simplest form.

(a) Evaluate the following expression: \( \left[ \left( 3\frac{1}{2} - 1.2 \right) \div \frac{23}{100} \right] \times \left( \frac{1}{4} + 0.15 \right) \).
(b) A water tank contains \( 15\frac{3}{5} \) litres of water. A gardener uses \( 4.8 \) litres of water to water his flowers. He then pours \( \frac{3}{4} \) of the remaining water into several identical small bottles. If each small bottle has a capacity of \( 0.45 \) litres, how many bottles can be completely filled?